Photosynthetic carbon dioxide assimilation provides the carbon input to ecosystems from the atmosphere and also regulates leaf temperature and transpiration through stomatal conductance. Current representations of these processes in terrestrial biosphere models link the dependencies of leaf biophysics with the biochemistry of photosynthesis. This chapter develops the physiological foundation and mathematical equations to describe photosynthesis for C3 and C4 plants. While the equations that describe C3 photosynthesis are fairly well understood, key parameters are less well known. Moreover, terrestrial biosphere models can differ greatly in how they implement the photosynthesis equations. C4 photosynthesis is less well understood for global models.